How good is your money maths?

Former_MSE_Lee

Poll started 22 November 2011, click here to vote

How good is your money maths?

Every few years we ask this poll – to see how good people are at figuring out a basic, but not straightforward money sum.

Which of these scenarios about the stock market gives the best return?

A. It rises 10% a year for 4 years then drops 10% a year for 4 years
B. It drops 10% a year for 4 years then rises 10% a year for 4 years
C. The market stays the same
D. All the above answers are equal


[FONT=&quot]Here's Martin's explanation[/FONT]:

[FONT=&quot]
[/FONT]
The answer is C. The market stays the same.
First let me give you the numerical answer:

Option A. Rises 10%/year for 4 years then drops 10%/year for 4 years. END RESULT: 96% of the start value.
Option B. Falls 10%/year for 4 years then rises 10%/year for 4 years. END RESULT: 96% of the start value.
Option C. The market stays the same. END RESULT: 100% of the start value.
Option D. All the above answers are equal. NOT TRUE AS A, B & C produce different answers.

Now on to why:

The most important thing to understand is that if you add X% on a value then take X% off – you'll always end up with less than you started with.

If algebra is confusing lets try again this time with an example. You have £100 and get 20% on it. Now you've £120, but then you take 20% off that and (as 20% of £120 is £24) you've only £96 left.

The reason this works is because you're taking 20% off a bigger number than you're adding 20% too.

And this is commutative (it works both ways round) so let's do it the other way. You start with 100 and take 20% off, now you've £80, then you add 20% to £80 and you get £96. This is because again you're adding the 20% to a smaller number than you're taking it off.

Hope that helps. If you're not sure try it on a calculator yourself.

Click reply to discuss

mattytun

I went for D. All are equal.............:o

Sarita

Hi Lee (admin who posted this)
As I write there have been 180s view and no comments or discussion. It would be helpful if you kicked off with an explanation of why (spoiler alert) C- 'stays the same' is the right answer. I assume the point of this thread is to educate your visitors not leave them confused & bamboozled!
It wasn't clear from the question whether the shares were being sold at the end of this period, or whether it was a matter of income from dividends (how could one guage that?!) ~ I am part of the bamboozled brigade so please enlighten us.
Cheers,
Sarita

newuser27

Assuming you start with £100

a) and b) end up the same as they are essentially both = £100 x 1.1^4 x 0.9^4 = £96.06

c) you stay at £100

lilrahi

Yay I got it right

ffacoffipawb

MSE_Lee wrote: »

Poll started 22 November 2011, click here to vote

How good is your money maths?

Every few years we ask this poll – to see how good people are at figuring out a basic, but not straightforward money sum.

Which of these scenarios about the stock market gives the best return?

A. It rises 10% a year for 4 years then drops 10% a year for 4 years
B. It drops 10% a year for 4 years then rises 10% a year for 4 years
C. Stays the same
D. All are equal


[FONT=&quot]Here's Martin's explanation[/FONT]:[FONT=&quot]
[/FONT]
Click reply to discuss

The spoiler uses 5% instead of 10% (obviously has no effect on the result)

pjsmiffy

I had to put it through excel .
on a 10k example you loose a 1/100 of a penny less if the gain comes first. But that could be the rounding error.

£9605.9601

Blubell

I got it right,thought it was pretty obvious.:T

tgroom57

Hooray for Excel !

Pmarmalade

pjsmiffy wrote: »

I had to put it through excel .
on a 10k example you loose a 1/100 of a penny less if the gain comes first. But that could be the rounding error.

£9605.9601

I, personally, would put that much time and effort into a poll. With these things I just have a guess, basically. If it was my own money dilemma I'd definitely invest the time and effort.

Alexandrason

Really don't think the answers/question were very clear here! The best return on the 4 scenarios, well to my mind only the first 2 were scenarios! It all could have been written better. It was very obvious that you would end up with less money than you started with for the a and b scenario, so c staying the same would be a better return than a and b as you haven't lost anything. But what the h*** does 'all are equal' mean??? Makes no sense! :-/